Sensitivity of bi-spectral retrievals to the fixed effective variance assumption in ship tracks

Abstract. Ship tracks, bright lines in clouds formed by ship exhaust, serve as “natural laboratories” for investigating aerosol-cloud interactions, one of the largest sources of uncertainty in the human forcing of the climate. Observing ship tracks has been used to help constrain the effect of anthropogenic aerosols on cloud brightness, amount and water content. The validity of these constraints relies, in part, on the accuracy of satellite retrieval algorithms used to measure cloud properties. A known source of uncertainty in these algorithms is the representation of the droplet size distribution. Standard bi-spectral retrievals (e.g. MODIS) rely on a fixed effective variance (veff) for the modified gamma distribution used to model cloud droplet dispersion. The introduction of aerosols into clean, marine clouds produces not only smaller droplets but also a narrower size distribution, contradicting this fixed assumption. This study presents a controlled, synthetic retrieval experiment that isolates the sensitivity of cloud property retrievals, and the derived aerosol-cloud interaction metrics, to this single assumption. This study uses idealised ship tracks as the test case because they provide the strongest realistic contrast between the assumed and true distribution widths. The results produced indicate that neglecting the narrowing of the droplet size distribution causes retrieved effective radius (re) to differ systematically between clean and polluted regimes. The polluted branch is overestimated relative to the near-unbiased clean branch by approximately 2.3 %–3.4 %, depending on the assumed retrieval baseline. Optical depth (τ) is virtually unaffected in either regime. LWP is retrieved with little bias in either regime, so the clean-to-polluted LWP contrast is largely preserved. Nd shows the opposite problem. The apparent clean-to-polluted increase in Nd is overstated by 22 %–23 % under both operational assumptions. This discrepancy is driven by the inverse dependence of Nd on the spectral width parameter k, inflating the droplet count in narrow polluted distributions while underestimating it in broader clean ones. If the aerosol-driven narrowing of the droplet size distribution assumed here is representative of real ship tracks, this contrast inflation could exaggerate the apparent susceptibility of clouds to aerosols, contributing to an overstatement of the Twomey effect in observation-based estimates reliant on data from ship tracks. Under the same conditions, satellite-based monitoring of climate intervention efforts, such as marine cloud brightening, could similarly overestimate their efficacy.